JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (6): 77-83, 91.doi: 10.6040/j.issn.1671-9352.0.2022.469

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Continuous dependence of solution for impulsive evolution equations with infinite delay

Pan SUN(),Xuping ZHANG*()   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2022-09-01 Online:2023-06-20 Published:2023-05-23
  • Contact: Xuping ZHANG E-mail:psun0831@163.com;lanyu9986@126.com

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Abstract:

By comprehensive applying the theory of operator semigroups and method of nonlinear analysis, this paper will investigate the existence of mild solutions and the continuous dependence of mild solutions to initial values for the initial problem of impulsive evolution equations with infinite delay.

Key words: infinite delay, impulsive evolution equation, compact semigroup, continuous dependence of mild solution

CLC Number: 

  • O175.15
1 CHANG J C . Existence and compactness of solutions to impulsive differential equations with nonlocal conditions[J]. Mathematical Methods in the Applied Sciences, 2016, 39 (2): 317- 327.
doi: 10.1002/mma.3479
2 FU X L , CAO Y J . Existence for neutral impulsive differential inclusions with nonlocal conditions[J]. Nonlinear Analysis: Theory, Methods & Applications, 2008, 68 (12): 3707- 3718.
3 FU X L , ZHOU L . Stability for impulsive functional differential equations with infinite delays[J]. Acta Math Sin, 2010, 26 (5): 909- 922.
doi: 10.1007/s10114-009-7071-5
4 JI S C , LI G . Existence results for impulsive differential inclusions with nonlocal conditions[J]. Comput Math Appl, 2011, 62 (4): 1908- 1915.
5 SAMOILENKO A M , PERESTYUK N A . Impulsive differential equations[M]. Singapore: World Scientific, 1995.
6 ABADA N , BENCHOHRA M , HAMMOUCHE H . Existence results for semi-linear differential evolution equations with impulses and delay[J]. Cubo (Temuco), 2010, 12 (2): 1- 17.
doi: 10.4067/S0719-06462010000200001
7 BALACHANDRAN K , ANNAPOORANI N . Existence results for impulsive neutral evolution integro-differential equations with infinite delay[J]. Nonlinear Analysis: Hybrid Systems, 2009, 3 (4): 674- 684.
doi: 10.1016/j.nahs.2009.06.004
8 CHANG Y K , ANGURAJ A , ARJUNAN M M . Existence results for impulsive neutral functional differential equations with infinite delay[J]. Nonlinear Analysis: Hybrid Systems, 2008, 2 (1): 209- 218.
doi: 10.1016/j.nahs.2007.10.001
9 DONG Q X , LI G . Existence of solutions for nonlinear evolution equations with infinite delay[J]. Bull Korean Math Soc, 2014, 51 (1): 43- 54.
doi: 10.4134/BKMS.2014.51.1.043
10 HAO X N , LIU L S . Mild solution of semi-linear impulsive integro-differential evolution equation in Banach spaces[J]. Math Methods Appl, 2017, 40 (13): 4832- 4841.
11 刘洋, 范虹霞. 一类具有无穷时滞的抽象脉冲发展方程mild解的存在性[J]. 安徽师范大学学报(自然科学版), 2020, 43 (1): 11- 18.
LIU Yang , FAN Hongxia . Existence of mild solution for a class of abstract impulsive evolution equations with infinite delays[J]. Journal of Anhui Normal University (Natural Science), 2020, 43 (1): 11- 18.
12 WANG J R . Stability of noninstantaneous impulsive evolution equations[J]. Applied Mathematics Letters, 2017, 73, 157- 162.
doi: 10.1016/j.aml.2017.04.010
13 ZHANG X P , CHEN P Y , O'REGAN D . Continuous dependence of fuzzy mild solutions on parameters for IVP of fractional fuzzy evolution equations[J]. Fractional Calculus and Applied Analysis, 2021, 24 (6): 1758- 1776.
doi: 10.1515/fca-2021-0076
14 ZHU J B , FU X L . Existence and asymptotic periodicity of solutions for neutral integro-differential evolution equations with infinite delay[J]. Mathematica Slovaca, 2022, 72 (1): 121- 140.
doi: 10.1515/ms-2022-0009
15 ZHANG X P , LI Y X . Existence of solutions for delay evolution equations with nonlocal conditions[J]. Open Mathematics, 2017, 15 (1): 616- 627.
doi: 10.1515/math-2017-0055
16 CHANG Y K . Controllability of impulsive functional differential systems with infinite delay in Banach spaces[J]. Chaos, Solitions & Fractals, 2007, 33 (5): 1601- 1609.
17 YAN B Q . Boundary value problems on the half-line with impulses and infinite delay[J]. Journal of Mathematical Analysis and Applications, 2001, 259 (1): 94- 114.
doi: 10.1006/jmaa.2000.7392
18 尤秉礼. 常微分方程补充教程[M]. 北京: 人民教育出版社, 1982.
YOU B L . Ordinary differential equation complementary curriculum[M]. Beijing: People Education Press, 1982.
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